If you have the means to pay more rent up front, then you can negotiate an early payment discount. Maybe you can get 5% to 10% off your rent if you pay by the 20th of the prior month.
I recall that my property managers were almost always too busy to talk to tenants, and the supers were always overwhelmed with work. So why not ask the property manager if they need any help? If your property manager or landlord won’t lower your rent outright, doing some tasks around the apartment complex can earn you a nice rent reduction. :)
See if your landlord has a smaller unit available. If you are in a one bedroom, for example, maybe you can move to a studio to reduce the rent.
The carrot Bill refers to is significant. Add to that list offering to PAINT the exterior in exchange for a $150 a month ($1,800 a year) reduction. And this may continue for multiple years...that adds up.
Be aware, their is a growing shortage of affordable rental housing.
It's been done, but there are no guarantees unless you decide not to ask. Offer what you can, let them accept, decline or offer a compromise. Maybe you start at your budget now for 6 months and it goes up to the advertised rent for the next 6 months after you've had a raise.